You are completely right to stick with what works, and you definitely do not need to skin your fish before frying it in a skillet. Your grandma's method of dusting skin-on fish with a bit of flour and frying it up in a cast iron skillet is a time-tested technique that produces delicious results.
Leaving the skin on serves a few wonderful purposes. First, crispy fish skin tastes fantastic and adds a great texture to the meal. Second, the skin acts as a natural protective barrier that keeps the delicate flesh moist and helps hold the fillet together so it does not fall apart while cooking. As long as the fish has been properly scaled, leaving the skin on is not only fine, but often preferred by cooks.
The reason you see modern recipes calling for skinning or scoring usually comes down to a few specific situations. Some types of fish have tough or strong-tasting skin that is unpleasant to eat. Furthermore, when heat hits fish skin, the collagen inside it quickly shrinks, which can cause thin fillets to curl up in the pan. Scoring the skin simply cuts those fibers to keep the fish flat. However, for a simple weeknight pan-fry, you can easily achieve the same result by just gently pressing the fillet down with a spatula for five to ten seconds when it first hits the hot pan.
For a quick homestyle meal, there is no need to make things complicated. Pat the fish dry, leave the skin on, dredge it in flour, and start frying skin-side down in your skillet. You will have a crisp, delicious dinner on the table without any extra fuss.